Negative Binomial Experiment

Each trial can result in just two possible outcomes. We call one of these
outcomes a success and the other, a failure.

The probability of success, denoted by p, is the same on every
trial.

The trials are independent;
that is, the outcome on one trial does not affect the outcome on other trials.

The experiment continues until r successes are observed, where r
is specified in advance.

Consider the following statistical experiment. You flip a coin repeatedly and count
the number of times the coin lands on heads. You continue flipping the coin until
it has landed 5 times on heads. This is a negative binomial experiment
because:

The experiment consists of repeated trials. We flip a coin repeatedly until it
has landed 5 times on heads.

Each trial can result in just two possible outcomes - heads or tails.

The probability of success is constant - 0.5 on every trial.

The trials are independent; that is, getting heads on one trial does not affect
whether we get heads on other trials.

The experiment continues until a fixed number of successes have occurred;
in this case, 5 heads.